Physical Aspects of Fruit Growth : THEORETICAL ANALYSIS OF DISTRIBUTION OF SURFACE GROWTH FORCES IN FRUIT IN RELATION TO CRACKING AND SPLITTING

Russeting of Fruits: Etiology and Management

The skin of a fruit protects the vulnerable, nutrient-rich flesh and seed(s) within from the hostile environment. It is also responsible for the fruit’s appearance. In many fruitcrop species, russeting compromises fruit appearance and thus commercial value. Here, we review the literature on fruit russeting, focusing on the factors and mechanisms that induce it and on the management and breeding strategies that may reduce it. Compared with a primary fruit skin, which is usually distinctively colored and shiny, a secondary fruit skin is reddish-brown, dull and slightly rough to the touch (i.e., russeted). This secondary skin (periderm) comprises phellem cells with suberized cell walls, a phellogen and a phelloderm. Russeted (secondary) fruit skins have similar mechanical properties to non-russeted (primary) ones but are more plastic. However, russeted fruit skins are more permeable to water vapor, so russeted fruits suffer higher postharvest water loss, reduced shine, increased shrivel and reduced packed weight (most fruit is sold per kg). Orchard factors that induce russeting include expansion-growth-induced strain, surface wetness, mechanical damage, freezing temperatures, some pests and diseases and some agrochemicals. All these probably act via an increased incidence of cuticular microcracking as a result of local concentrations of mechanical stress. Microcracking impairs the cuticle’s barrier properties. Potential triggers of russeting (the development of a periderm), consequent on cuticular microcracking, include locally high concentrations of O2, lower concentrations of CO2 and more negative water potentials. Horticulturists sometimes spray gibberellins, cytokinins or boron to reduce russeting. Bagging fruit (to exclude surface moisture) is also reportedly effective. From a breeding perspective, genotypes having small and more uniform-sized epidermal cells are judged less likely to be susceptible to russeting.

Cuticle and skin cell walls have common and unique roles in grape berry splitting

The skin protects a fruit from environmental stresses and supports the fruit's structure. Failure of the skin leads to fruit splitting and may compromise commercial production for fruit growers. The mechanical properties of the cuticle and skin cell walls might influence the splitting susceptibility of fleshy fruits. Thin shell theory and fracture mechanics were utilized in this study to target the potential factors contributing to splitting susceptibility. The study analyzed the structure of the cuticle and epidermis in ripening grape berries and examined the temporal dynamics of berry splitting. Cuticular waxes were partially removed, and skin cell walls were manipulated using wall stiffening and loosening solutions that altered reactions involving hydrogen peroxide. A more than twofold difference in cuticle thickness among grape cultivars did not account for their differences in splitting resistance. However, while removing predominantly epicuticular wax did not alter the berries' splitting resistance, their surface appearance and increasing yield strength following partial wax removal support the notion that cuticular waxes contribute to berry mechanical properties. Immersing berries in H₂O₂-based cell wall loosening solutions increased the splitting probability and accelerated berry splitting, whereas cell wall stiffening solutions decreased the splitting probability and delayed berry splitting. These results showed that both cuticle and skin cell walls contribute to the mechanical properties of grape berries and to their splitting resistance. The results also suggest that the two current explanations for fruit splitting, the critical turgor model and the zipper model, should be viewed as complementary rather than incompatible.

LncRNA regulates tomato fruit cracking by coordinating gene expression via a hormone-redox-cell wall network

BACKGROUND

Fruit cracking occurs easily under unsuitable environmental conditions and is one of the main types of damage that occurs in fruit production. It is widely accepted that plants have developed defence mechanisms and regulatory networks that respond to abiotic stress, which involves perceiving, integrating and responding to stress signals by modulating the expression of related genes. Fruit cracking is also a physiological disease caused by abiotic stress. It has been reported that a single or several genes may regulate fruit cracking. However, almost none of these reports have involved cracking regulatory networks.

RESULTS

Here, RNA expression in 0 h, 8 h and 30 h saturated irrigation-treated fruits from two contrasting tomato genotypes, 'LA1698' (cracking-resistant, CR) and 'LA2683' (cracking-susceptible, CS), was analysed by mRNA and lncRNA sequencing. The GO pathways of the differentially expressed mRNAs were mainly enriched in the 'hormone metabolic process', 'cell wall organization', 'oxidoreductase activity' and 'catalytic activity' categories. According to the gene expression analysis, significantly differentially expressed genes included Solyc02g080530.3 (Peroxide, POD), Solyc01g008710.3 (Mannan endo-1,4-beta-mannosidase, MAN), Solyc08g077910.3 (Expanded, EXP), Solyc09g075330.3 (Pectinesterase, PE), Solyc07g055990.3 (Xyloglucan endotransglucosylase-hydrolase 7, XTH7), Solyc12g011030.2 (Xyloglucan endotransglucosylase-hydrolase 9, XTH9), Solyc10g080210.2 (Polygalacturonase-2, PG2), Solyc08g081010.2 (Gamma-glutamylcysteine synthetase, gamma-GCS), Solyc09g008720.2 (Ethylene receptor, ER), Solyc11g042560.2 (Ethylene-responsive transcription factor 4, ERF4) etc. In addition, the lncRNAs (XLOC_16662 and XLOC_033910, etc) regulated the expression of their neighbouring genes, and genes related to tomato cracking were selected to construct a lncRNA-mRNA network influencing tomato cracking.

CONCLUSIONS

This study provides insight into the responsive network for water-induced cracking in tomato fruit. Specifically, lncRNAs regulate the hormone-redox-cell wall network, including plant hormone (auxin, ethylene) and ROS (H2O2) signal transduction and many cell wall-related mRNAs (EXP, PG, XTH), as well as some lncRNAs (XLOC_16662 and XLOC_033910, etc.).

Spatial heterogeneity of flesh-cell osmotic potential in sweet cherry affects partitioning of absorbed water

A fleshy fruit is commonly assumed to resemble a thin-walled pressure vessel containing a homogenous carbohydrate solution. Using sweet cherry (Prunus avium L.) as a model system, we investigate how local differences in cell water potential affect H2O and D2O (heavy water) partitioning. The partitioning of H2O and D2O was mapped non-destructively using magnetic resonance imaging (MRI). The change in size of mesocarp cells due to water movement was monitored by optical coherence tomography (OCT, non-destructive). Osmotic potential was mapped using micro-osmometry (destructive). Virtual sections through the fruit revealed that the H2O distribution followed a net pattern in the outer mesocarp and a radial pattern in the inner mesocarp. These patterns align with the disposition of the vascular bundles. D2O uptake through the skin paralleled the acropetal gradient in cell osmotic potential gradient (from less negative to more negative). Cells in the vicinity of a vascular bundle were of more negative osmotic potential than cells more distant from a vascular bundle. OCT revealed net H2O uptake was the result of some cells loosing volume and other cells increasing volume. H2O and D2O partitioning following uptake is non-uniform and related to the spatial heterogeneity in the osmotic potential of mesocarp cells.

A Development-Associated Decrease in Osmotic Potential Contributes to Fruit Ripening Initiation in Strawberry (Fragaria ananassa)

Fruit development and ripening are accompanied by a large increase in cellular soluble solid contents, which results in a significant decrease in osmotic potential (DOP). Here, we report that this development-associated DOP contributes to the initiation of ripening in strawberry (Fragaria ananassa Duch., Benihoppe) fruit. We show that fruit water potential significantly decreases at the onset of ripening as a result of the DOP. Further analysis using nuclear magnetic resonance spectroscopy (NMR) indicated that the change in fruit water potential was likely caused by catabolism of large molecules in receptacle cells, and bioinformatic analysis identified a family of osmotin-like proteins (OLP) that have a potential role in osmolyte accommodation. The gene expression of more than half of the OLP members increased substantially at the onset of fruit ripening, and specifically responded to DOP treatment, consistent with a close relationship between DOP and fruit ripening. We report that the DOP induced either by mannitol or water loss, triggered fruit ripening, as indicated by the elevated expression of multiple ripening genes and diverse ripening-associated physiological parameters. Collectively, these results suggest that the DOP contributes to strawberry fruit ripening initiation.

Cytokinin treatment modifies litchi fruit pericarp anatomy leading to reduced susceptibility to post-harvest pericarp browning

Litchi (Litchi chinensis Sonn.) is a subtropical fruit known for its attractive red pericarp color, semi-translucent white aril and unique flavor and aroma. Rapid post-harvest pericarp browning strictly limits litchi fruit marketing. In the current research, we hypothesized that modification of litchi fruit pericarp anatomy by hormone application may reduce fruit susceptibility to post-harvest pericarp browning. In this context, we hypothesized that cytokinin treatment, known to induce cell division, may yield fruit with thicker pericarp and reduced susceptibility for fruit surface micro-crack formation, water loss and post-harvest pericarp browning. Exogenous cytokinin treatment was applied at different stages along the course of litchi fruit development and the effect on fruit pericarp anatomy, fruit maturation and postharvest pericarp browning was investigated. Interestingly, cytokinin treatment, applied 4 weeks after full female bloom (WFB), during the phase of pericarp cell division, led to mature fruit with thicker pericarp, reduced rate of post-harvest water loss and reduced susceptibility to post-harvest pericarp browning, as compared to non-treated control fruit. Histological sections ascribe the difference in pericarp anatomy to increased cell proliferation in the parenchymatic tissue and the highly-lignified brachysclereid cell layer. In contrast, exogenous cytokinin treatment applied 7 WFB, following the phase of pericarp cell division, significantly increased epidermal-cell proliferation but had no significant effect on overall fruit pericarp thickness and only minor affect on post-harvest water loss or pericarp browning. Interestingly, the late cytokinin treatment also significantly postponed fruit maturation-associated anthocyanin accumulation and chlorophyll degradation, as previously reported, but had no effect on other parameters of fruit maturation, like total soluble sugars and total titratable acids typically modified during aril maturation. In conclusion, exogenous cytokinin treatment at different stages in fruit development differentially modifies litchi fruit pericarp anatomy by induction of cell-type specific cell proliferation. Early cytokinin treatment during the phase of pericarp cell division may prolong litchi fruit storage by reducing fruit susceptibility to post-harvest water loss and pericarp browning.

Localized bursting of mesocarp cells triggers catastrophic fruit cracking

The so-called rain-cracking of sweet cherry fruit severely threatens commercial production. Simple observation tells us that cuticular microcracking (invisible) always precedes skin macrocracking (visible). The objective here was to investigate how a macrocrack develops. Incubating detached sweet cherry fruit in deionized water induces microcracking. Incubating fruit in D₂O and concurrent magnetic resonance imaging demonstrates that water penetration occurs only (principally) through the microcracks, with nondetectable amounts penetrating the intact cuticle. Optical coherence tomography of detached, whole fruit incubated in deionized water, allowed generation of virtual cross-sections through the zone of a developing macrocrack. Outer mesocarp cell volume increased before macrocracks developed but increased at a markedly higher rate thereafter. Little change in mesocarp cell volume occurred in a control zone distant from the crack. As water incubation continued, the cell volume in the crack zone decreased, indicating leaking/bursting of individual mesocarp cells. As incubation continued still longer, the crack propagated between cells both to form a long, deep macrocrack. Outer mesocarp cell turgor did not differ significantly before and after incubation between fruit with or without macrocracks; nor between cells within the crack zone and those in a control zone distant from the macrocrack. The cumulative frequency distribution of the log-transformed turgor pressure of a population of outer mesocarp cells reveals all cell turgor data followed a normal distribution. The results demonstrate that microcracks develop into macrocracks following the volume increase of a few outer mesocarp cells and is soon accompanied by cell bursting.

Cell wall swelling, fracture mode, and the mechanical properties of cherry fruit skins are closely related

Cell wall swelling, fracture mode (along the middle lamellae vs. across cell walls), stiffness, and pressure at fracture of the sweet cherry fruit skin are closely related. Skin cracking is a common phenomenon in many crops bearing fleshy fruit. The objectives were to investigate relationships between the mode of fracture, the extent of cell wall swelling, and the mechanical properties of the fruit skin using sweet cherry (Prunus avium) as a model. Cracking was induced by incubating whole fruit in deionised water or by fracturing exocarp segments (ESs) in biaxial tensile tests. The fracture mode of epidermal cells was investigated by light microscopy. In biaxial tensile tests, the anticlinal cell walls of the ES fractured predominantly across the cell walls (rather than along) and showed no cell wall swelling. In contrast, fruit incubated in water fractured predominantly along the anticlinal epidermal cell walls and the cell walls were swollen. Swelling of cell walls also occurred when ESs were incubated in malic acid, in hypertonic solutions of sucrose, or in water. Compared to the untreated controls, these treatments resulted in more frequent fractures along the cell walls, lower pressures at fracture (p _fracture), and lower moduli of elasticity (E, i.e., less stiff). Conversely, compared to the untreated controls, incubating the ES in CaCl₂ and in high concentrations of ethanol resulted in thinner cell walls, in less frequent fractures along the cell walls, higher E and p _fracture. Our study demonstrates that fracture mode, stiffness, and pressure at fracture are closely related to cell wall swelling. A number of other factors, including cultivar, ripening stage, turgor, CaCl₂, and malic acid, exert their effects only indirectly, i.e., by affecting cell wall swelling.

Transient silencing of CHALCONE SYNTHASE during fruit ripening modifies tomato epidermal cells and cuticle properties

Tomato (Solanum lycopersicum) fruit ripening is accompanied by an increase in CHALCONE SYNTHASE (CHS) activity and flavonoid biosynthesis. Flavonoids accumulate in the cuticle, giving its characteristic orange color that contributes to the eventual red color of the ripe fruit. Using virus-induced gene silencing in fruits, we have down-regulated the expression of SlCHS during ripening and compared the cuticles derived from silenced and nonsilenced regions. Silenced regions showed a pink color due to the lack of flavonoids incorporated to the cuticle. This change in color was accompanied by several other changes in the cuticle and epidermis. The epidermal cells displayed a decreased tangential cell width; a decrease in the amount of cuticle and its main components, cutin and polysaccharides, was also observed. Flavonoids dramatically altered the cuticle biomechanical properties by stiffening the elastic and viscoelastic phase and by reducing the ability of the cuticle to deform. There seemed to be a negative relation between SlCHS expression and wax accumulation during ripening that could be related to the decreased cuticle permeability to water observed in the regions silencing SlCHS. A reduction in the overall number of ester linkages present in the cutin matrix was also dependent on the presence of flavonoids.

Review: computer vision applied to the inspection and quality control of fruits and vegetables

This is a review of the current existing literature concerning the inspection of fruits and vegetables with the application of computer vision, where the techniques most used to estimate various properties related to quality are analyzed. The objectives of the typical applications of such systems include the classification, quality estimation according to the internal and external characteristics, supervision of fruit processes during storage or the evaluation of experimental treatments. In general, computer vision systems do not only replace manual inspection, but can also improve their skills. In conclusion, computer vision systems are powerful tools for the automatic inspection of fruits and vegetables. In addition, the development of such systems adapted to the food industry is fundamental to achieve competitive advantages.

Fruit ripening in Vitis vinifera: apoplastic solute accumulation accounts for pre-veraison turgor loss in berries

In Vitis vinifera L. berries, the onset of ripening (known as "veraison") involves loss of turgor (P) in the mesocarp cells. We hypothesized that P loss was associated with an accumulation of apoplastic solutes in mesocarp tissue prior to veraison. Apoplastic sap was extracted from the mesocarp by centrifugation at the appropriate gravity to measure the apoplast solute potential (Psi (s) (A) ) and assay the sap composition. The Psi (s) (A) was about -0.2 MPa early in development, decreased about 1.0 MPa by veraison, and continued to decrease during ripening to almost -4.0 MPa by the end of berry development. Potassium, malate, tartrate, proline, glucose, fructose, and sucrose were quantified in apoplastic sap. The calculated contribution of these solutes was about 50% of the total Psi (s) (A) preveraison, but increased to about 75% as fructose and glucose accumulated during ripening. The contribution of the estimated matric potential to apoplast water potential decreased during development and was only 1.5% postveraison. We conclude that high concentrations of solutes accumulated in the mesocarp apoplast prior to veraison, and that P loss was a direct result of decreased Psi (s) (A) . Because Psi (s) (A) decreased before veraison, our findings suggest that apoplast solutes play an important role in the events of cellular metabolism that lead to the onset of ripening.

Direct in situ measurement of cell turgor in grape (Vitis vinifera L.) berries during development and in response to plant water deficits

Vitis vinifera L. berries are non-climacteric fruits that exhibit a double-sigmoid growth pattern, and at the point known as 'veraison', which is just before the beginning of the second period of rapid fruit growth, these berries undergo several abrupt physiological changes. Cell pressure probe was used to examine the in situ turgor (P) of cells in the mesocarp during berry development and in response to plant water deficits. Initial tests comparing attached and detached berries demonstrated that cell P was stable for up to 48 h after detachment from the vine, provided that water loss from the berry was prevented. Cell P at pre-dawn was on the order of 0.25 MPa pre-veraison (PreV) and was reduced by an order of magnitude to 0.02 MPa post veraison (PostV). Cell P declined slightly but significantly with depth from the berry surface PreV, but not PostV. When water was withheld from potted vines, cell P declined about 0.2 Mpa, as pre-dawn vine water potential declined about 0.6 MPa over 12 d, whereas cell P was completely insensitive to a 1.10 MPa decrease in pre-dawn vine water potential after veraison. Rewatering of stressed plants also resulted in a 24 h recovery of cell P before, but not after veraison. The substantial decline in cell P around veraison is consistent with the decline in berry firmness that is known to occur at this time, and the PostV insensitivity of P to changes in vine water status is consistent with current hypotheses that the PostV berry is hydraulically isolated from the vine. The fact that a measurable P of about 0.02 MPa and typical cell hydraulic/osmotic behaviour were exhibited in PostV berries, however, indicates that cell membranes remain intact after veraison, contrary to many current hypotheses that veraison is associated with a general loss of membrane function and cellular compartmentation in the grape berry. We hypothesize that cell P is low in the PostV berry, and possibly other fleshy fruits, because of the presence of regulated quantities of apoplastic solutes.

Modelling the effect of fruit growth on surface conductance to water vapour diffusion

BACKGROUND AND AIMS

A model of fruit surface conductance to water vapour diffusion driven by fruit growth is proposed. It computes the total fruit conductance by integrating each of its components: stomata, cuticle and cracks.

METHODS

The stomatal conductance is computed from the stomatal density per fruit and the specific stomatal conductance. The cuticular component is equal to the proportion of cuticle per fruit multiplied by its specific conductance. Cracks are assumed to be generated when pulp expansion rate exceeds cuticle expansion rate. A constant percentage of cracks is assumed to heal each day. The proportion of cracks to total fruit surface area multiplied by the specific crack conductance accounts for the crack component. The model was applied to peach fruit (Prunus persica) and its parameters were estimated from field experiments with various crop load and irrigation regimes.

KEY RESULTS

The predictions were in good agreement with the experimental measurements and for the different conditions (irrigation and crop load). Total fruit surface conductance decreased during early growth as stomatal density, and hence the contribution of the stomatal conductance, decreased from 80 to 20 % with fruit expansion. Cracks were generated for fruits exhibiting high growth rates during late growth and the crack component could account for up to 60 % of the total conductance during the rapid fruit growth. The cuticular contribution was slightly variable (around 20 %). Sensitivity analysis revealed that simulated conductance was highly affected by stomatal parameters during the early period of growth and by both crack and stomatal parameters during the late period. Large fruit growth rate leads to earlier and greater increase of conductance due to higher crack occurrence. Conversely, low fruit growth rate accounts for a delayed and lower increase of conductance.

CONCLUSIONS

By predicting crack occurrence during fruit growth, this model could be helpful in managing cropping practices for integrated plant protection.

Two-dimensional tension tests in plant biomechanics--sweet cherry fruit skin as a model system

Splitting of fruits is a function of two-dimensional tension caused by different growth rates of tissues and turgor, especially water uptake shortly before harvest. In order to analyse the mechanical properties of spheroid plant material close to stress-strain conditions in vivo, a new hydraulic two-dimensional testing device was set up. Sweet cherry (Prunus avium L.) fruit skin was chosen as a model system. The recorded pressure-deflection curves were non-linear, with a considerable initial "lag phase" and a distinct increasing end part. Taking into account the special geometry, these curves could be modelled with a newly developed analytical approach based on linear elastic material behaviour. The results demonstrated good correlation if a modulus of elasticity ranging from 160 to 250 MPa for the cherry fruit skin was chosen. In addition, a mean strength value of 47 MPa was calculated based on the theory of thin shells and spheres. The results are compared with mechanical data found for fruits and other plant material. In order to test the theoretical approach, two- and one-dimensional tension tests were performed on packaging PE foil, revealing a mean modulus of 171 MPa in bi-axial tension, and 193 and 242 MPa in uni-axial tension, depending on the test speed. The results demonstrate that it seems to be feasible to use this method to analyse the two-dimensional stress-strain conditions of spheroid plant materials such as cherry fruit skins. It may be applied as a tool for crop testing to elucidate the mechanical basis of cracking susceptibility of fruits.

Changes in strain and deposition of cuticle in developing sweet cherry fruit

Changes in surface area, deposition and elastic strain of the cuticular membrane (CM) were monitored during development of sweet cherry (Prunus avium L.) fruit. Fruit mass and surface area ('Sam') increased in a sigmoidal pattern between 16 and 85 days after full bloom (DAFB) with maximum rates of 0.35 g day(-1) and 0.62 cm(2) day(-1), respectively. Rates of total area strain, namely the sum of elastic plus plastic strain, were highest in cheek and stem cavity regions followed by stylar and suture regions. Rates of total uniaxial strain were higher in transverse, namely perpendicular to the stem/stylar axis, than in longitudinal direction, namely parallel to the stem/stylar axis. On a whole fruit basis CM mass remained essentially constant during fruit development. Mass of CM, dewaxed CM and wax per unit surface area decreased during development, particularly between 43 and 71 DAFB. There was no change in wax content of isolated CM. Up to 43 DAFB the surface area of isolated CM was similar to the area prior to excision indicating little elastic strain, but markedly decreased thereafter. Calculating elastic and plastic components of total strain of the CM revealed, that initial deformation up to 22 to 43 DAFB was mostly plastic. Thereafter, elastic strain was evident and both, elastic and plastic deformation, increased linearly with an increase in total strain. There was no consistent difference in the relative contribution of elastic strain to total strain between transverse and longitudinal directions, but both total and elastic strain were larger in the transverse direction. Abrading the CM had only little effect on fruit turgor. However, turgor decreased when the exocarp was cut indicating that the exocarp provided a significant structural shell of a mature sweet cherry fruit ('Regina'). Our data demonstrate, that (1) surface area expansion in sweet cherry fruit causes elastic and plastic strain of the CM, and (2) the onset of elastic strain coincided with the cessation of CM formation.

Studies on water transport through the sweet cherry fruit surface: III. Conductance of the cuticle in relation to fruit size

Rain-cracking of sweet cherry fruit has been related to water absorption through the fruit surface and large fruit has been reported to be more susceptible to cracking than small fruit. Therefore, the effect of fruit size on water conductance of the cuticular membrane (CM) of exocarp segments excised from cheek, suture or stylar end region of mature sweet cherry fruit (Prunus avium L. cv. Sam) was investigated. Segments consisting of epidermis, hypodermis and several layers of mesocarp cells were mounted in diffusion cells filled with deionized water. Mass loss due to transpiration was monitored gravimetrically during an 8-h incubation period (25 +/- 2 degrees C) over dry silica in the dark. Conductance was calculated from the amount of water transpired per unit surface area and time divided by the difference in water vapour concentration across the segment. For an average size cv. Sam sweet cherry CM conductance was 1.06 x 10-4, 0.91 x 10-4 and 2.09 x 10-4 m s-1 in cheek, suture and stylar end region, respectively. Fruit size had no significant effect on conductance in cheek or suture regions, but for the stylar end region conductance was positively related to fruit size. Stomatal density in the cheek, but not the suture or stylar end region increased as fruit size increased. The area of the stylar scar was positively related to fruit size. Conductance of the stylar scar averaged 37.6 +/- 4.0 x 10-4 m s-1 and was 54-fold higher than that of the CM between stomata in the cheek region (mean 0.69 x 10-4 m s-1). Conductance calculated on a whole fruit basis is estimated to increase by 108% as fruit size increases from 6 to 12 g. Increased conductance on a whole fruit basis may be attributed to increased fruit surface area and increased conductance per unit fruit surface area, particularly in the stylar end region.

Physical Aspects of Fruit Growth: STRESS DISTRIBUTION AROUND LENTICELS

The skin around a lenticel on a soft fruit has been modelled as a thin elastic plate with a rigid circular inclusion and applied tensile loads at the edges. A solution for the stress distribution in the skin has then been found using the linear theory of elasticity. From that solution the severity of the stress concentration and the location and form of initial cuticular failure have been deduced, the latter two being in broad agreement with observed crack initiation in the cuticle of grapes.